$$\dfrac{1}{25}(x+5)(x-5)(x-1)=\dfrac{x^3-x^2-25x+25}{25}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{25}(x+5)(x-5)(x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{x+5}{25}(x-5)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{x^2-25}{25}(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{x^3-x^2-25x+25}{25}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{1}{25} $ by $ x+5 $ to get $ \dfrac{ x+5 }{ 25 } $. Step 1: Write $ x+5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{25} \cdot x+5 & \xlongequal{\text{Step 1}} \frac{1}{25} \cdot \frac{x+5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( x+5 \right) }{ 25 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x+5 }{ 25 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{x+5}{25} $ by $ x-5 $ to get $ \dfrac{x^2-25}{25} $. Step 1: Write $ x-5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{x+5}{25} \cdot x-5 & \xlongequal{\text{Step 1}} \frac{x+5}{25} \cdot \frac{x-5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( x+5 \right) \cdot \left( x-5 \right) }{ 25 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2 -\cancel{5x}+ \cancel{5x}-25 }{ 25 } = \frac{x^2-25}{25} \end{aligned} $$ |
| ③ | Multiply $ \dfrac{x^2-25}{25} $ by $ x-1 $ to get $ \dfrac{ x^3-x^2-25x+25 }{ 25 } $. Step 1: Write $ x-1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{x^2-25}{25} \cdot x-1 & \xlongequal{\text{Step 1}} \frac{x^2-25}{25} \cdot \frac{x-1}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( x^2-25 \right) \cdot \left( x-1 \right) }{ 25 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^3-x^2-25x+25 }{ 25 } \end{aligned} $$ |